A Posteriori Error Estimates for a Nonconforming Finite Element Discretization of the Stokes–Biot System

Abstract

This paper presents an a posteriori error estimator for a (piecewise linear) nonconforming finite element approximation of the problem defining the interaction between a free fluid and poroelastic structure. The free fluid is governed by the Stokes equations, while the flow in the poroelastic medium is modeled using the Biot poroelasticity system. Equilibrium and kinematic conditions are imposed on the interface. The approach utilizes the same nonconforming Crouzeix–Raviart element discretization on the entire domain. For this discretization, we derive a residual indicator based on the jumps of the normal derivative of the nonconforming approximation. Lower and upper bounds form the main results with minimal assumptions on the mesh.